The extensive refurbishing of the sprawling 40-year-old James Creek public housing project in Southwest Washington, one of D.C.'s oldest and most threadbare, has finally been started, three years after the city received the first federal renovation funds.

During the intervening years the cost of gutting and rebuilding the interiors and replacing the roofs on the 267 two-story red brick row houses has ballooned from $7.1 million, city officials said.

The District was one of 33 cities which were selected in October 1978 for the Carter administration's $247-million comprehensive public housing modernization program designed to rebuild some of this nation's shabbiest projects. Washington, Boston, Newark, Philadelphia and Los Angeles County are among the last cities to spend their funds, according to Department of Housing and Urban Development (HUD) officials.

D.C. Mayor Marion Barry made only one oblique reference to the delays yesterday as he spoke at the project's groundbreaking ceremonies. The audience of about 60 included more city housing department employes than James Creek residents.

"You have been told for such a long time that the train is coming and nothing every arrives," he said. "This train has come."

Some James Creek residents said they would not believe the promises of new homes, with new kitchen appliances, bathrooms, plumbing and electrical wiring, until they occupy them.

"I think it's one of the best things to do to fix up these places, if we move back," said Emily Lynch, 40, who has lived at James Creek with her husband and three children since 1965. "I won't believe it until I see my new house."

Her neighbor, Lenore Hopkins, 33, agreed. "I think it's fine, if they follow through on the plans and complete all the houses. It will be nice to have new appliances."

Lynch said she was moved from her old apartment to another at James Creek last November and told by housing officials that the start of construction was imminent. She said work started about a month ago.

City housing director Robert L. Moore attributed the delays to HUD requirements and tenant participation in designing the new units.

HUD required the housing department to submit plans for repaying the $19 million it had overspent in city funds over the last eight to 10 years and for improving tenant selection, rent collections and skills of property managers. The preparation and approval of these plans took about eight months, Moore said.

The city also plans to hire two newly formed tenant-run corporations, which will hire other tenants to paint the new units and move tenants to temporary housing while their units are redone. The contracts will total $500,000, Moore said.

Housing officials have also required that all tenants, most of whom are unmarried women who have two or three children and receive public assistance, participate in a new "family development program" to improve their housekeeping and skills in being a parent.

"If you don't go to this program you don't move back," Moore told the audience. "We will be better housekeepers as we move back. We will be better parents as we move back. Too many times people think once we spend this money in five years it will look like it does today. That won't happen. Public housing is not a place for people who do not want to live decent."

Rents, which range from $10 to $299 a month, will not increase because public housing tenants pay no more than 25 percent of their income for their apartments. But they will begin to pay their own utility bills because new apartments will have individually metered utilities. HUD has required individual metering to reduce the cost of operating public housing.